Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#4666 |
| Fitting | C2×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×C22⋊C4 |
1360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(10,12,13,11)(15,17);(6,7,8,9)(10,11,13,12)(14,15)(16,17);(1,2)(4,5)(14,15)(16,17);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684779, #10684791, #10685173, … |
| maximal normal subgroup of | #10684779, #10684791, #10685173, … |
| maximal quotient of | C2×Dic3×#95, C4×#4666, C2×(C2×D3)⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5896);